Physics and Engineering of Radiation Detection

70 Chapter 2. Interaction of Radiation with Matter

The specific mean free path is generally quoted in units ofg/cm^2. In literature one
generally finds specific mean free paths for different media, which can then be simply
divided by the respective densities to obtain the actual mean free paths.

Example:

Compare the scattering mean free path of moderate energy electrons in

helium and argon under standard conditions of temperature and pressure.

The scattering cross section of electrons in helium and argon can be taken to

be 2. 9 × 107 band 1. 1 × 109 brespectively.

Solution:

For moderate energy electrons, we can use equation 2.1.11 to compute the

mean free path. SubstitutingT= 300K,P =1atm=1. 033 × 104 kg/m^2 ,

and the values ofNAandRin this equation yields

λm =

RT

√

2 NAPσ

=

(8.314)(300)

√

2(6. 022 × 1023 )(1. 033 × 104 )σ

=

2. 843 × 10 −^25

σ

The mean free paths in helium and argon are then given by

λm,hel =

2. 843 × 10 −^25

2. 9 × 10 −^21

=9. 8 × 10 −^5 m

=98μm

and λm,arg =

2. 843 × 10 −^25

1. 1 × 10 −^19

=2. 6 × 10 −^6 m

=2. 6 μm.

2.1.D RadiationLength.........................

We will see later in this chapter that the predominant mode of energy loss for
high energy electrons in matter is through a process calledBremsstrahlungand for
photons it ispair production. Both of these processes are intimately connected
by underlying physics and hence the overall attenuation of electrons and photons
passing through matter can be described by a single quantity calledradiation length.
Radiation length can be defined as the thickness of a material that an electron
travels such that it looses 1− 1 /e(corresponding to about 63%) of its energy by
Bremsstrahlung. Note that hereerefers to the exponential factor. For photons the
process would be pair production.
Radiation length is an extensively quoted quantity since it relates the physical
dimension of the material (such as its depth) to a property of radiation (such as its